NEW DELHI, May 27 (Reuters) - India's new Prime Minister Narendra Modi named Arun Jaitley as finance minister on Tuesday, tasking his close party colleague with reviving investment in an economy that has been growing at its slowest rate in a decade.

Jaitley, 61, will also lead the defence ministry as well as corporate affairs, the government said in a statement on Modi's cabinet that was sworn in on Monday.

Modi campaigned on a promise to cut bureaucratic sloth and fight corruption. Analysts say Modi's huge election victory gives him the mandate to advance reforms that stalled under the previous Congress-led, scandal-ridden administration of his prececessor, Manmohan Singh.

One of the top corporate lawyers in the country, Jaitley served as a commerce minister in a previous government of the Bharatiya Janata Party.

A day after his inauguration, Modi was due to meet Pakistan's Prime Minister Nawaz Sharif, who was among regional leaders invited to the ceremony, amid hopes of a thaw in ties between the two nuclear-armed countries.

Modi named BJP veteran Sushma Swaraj as foreign minister. The Hindu nationalist BJP has long advocated tough positions on national security and Pakistan, in particular.